Optimal stacking sequency in composite laminated plates for maximum strength using smooth angle distribution

Resumo

This study addresses the challenge of determining the optimal stacking sequence in laminated composite plates with specified thickness and layer properties, aiming to maximize strength according to the quadratic Tsai-Wu criterion. It is well established that directly optimizing the fiber orientation angles is a difficult task, mainly due to the proliferation of local minima, which increases sharply with the number of plies.
To overcome this issue, the paper proposes a novel strategy: an auxiliary problem is first solved, where the fiber orientation is modeled as a continuous distribution across the plate thickness. This distribution is defined by a smooth C∞ function governed by a small set of parameters, which serve as the primary optimization variables. This reduced formulation is shown to have relatively few local minima, making it an effective first step to generate laminates with an arbitrary number of layers. Unlike many existing methods, this approach does not confine the lamination space to regular patterns such as [(a/−a)n]s, which are often imposed to make optimization feasible.
The proposed method is validated on a benchmark problem involving a symmetric thin plate model with a known analytical solution. A genetic algorithm is employed for the optimization process. The results demonstrate that laminates with an arbitrary number of layers can be effectively optimized using the genetic algorithm, achieving consistent outcomes and rapid convergence.